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Leo Harrington [17]Leo A. Harrington [7]
  1. Peter A. Cholak, Rodney Downey & Leo A. Harrington (2008). The Complexity of Orbits of Computably Enumerable Sets. Bulletin of Symbolic Logic 14 (1):69 - 87.
    The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...)
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  2. Gregory Cherlin, Alan Dow, Yuri Gurevich, Leo Harrington, Ulrich Kohlenbach, Phokion Kolaitis, Leonid Levin, Michael Makkai, Ralph McKenzie & Don Pigozzi (2004). University of Illinois at Chicago, Chicago, IL, June 1–4, 2003. Bulletin of Symbolic Logic 10 (1).
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  3. Peter A. Cholak & Leo A. Harrington (2003). Isomorphisms of Splits of Computably Enumerable Sets. Journal of Symbolic Logic 68 (3):1044-1064.
    We show that if A and $\widehat{A}$ are automorphic via Φ then the structures $S_{R}(A)$ and $S_{R}(\widehat{A})$ are $\Delta_{3}^{0}-isomorphic$ via an isomorphism Ψ induced by Φ. Then we use this result to classify completely the orbits of hhsimple sets.
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  4. Peter A. Cholak & Leo A. Harrington (2002). On the Definability of the Double Jump in the Computably Enumerable Sets. Journal of Mathematical Logic 2 (02):261-296.
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  5. Peter A. Cholak & Leo A. Harrington (2000). Definable Encodings in the Computably Enumerable Sets. Bulletin of Symbolic Logic 6 (2):185-196.
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  6. Leo Harrington & Robert I. Soare (1998). Codable Sets and Orbits of Computably Enumerable Sets. Journal of Symbolic Logic 63 (1):1-28.
    A set X of nonnegative integers is computably enumerable (c.e.), also called recursively enumerable (r.e.), if there is a computable method to list its elements. Let ε denote the structure of the computably enumerable sets under inclusion, $\varepsilon = (\{W_e\}_{e\in \omega}, \subseteq)$ . We previously exhibited a first order ε-definable property Q(X) such that Q(X) guarantees that X is not Turing complete (i.e., does not code complete information about c.e. sets). Here we show first that Q(X) implies that X has (...)
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  7. Leo Harrington & Robert I. Soare (1998). Definable Properties of the Computably Enumerable Sets. Annals of Pure and Applied Logic 94 (1-3):97-125.
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  8. Rod Downey & Leo Harrington (1996). There is No Fat Orbit. Annals of Pure and Applied Logic 80 (3):277-289.
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  9. Leo Harrington & Robert I. Soare (1996). Definability, Automorphisms, and Dynamic Properties of Computably Enumerable Sets. Bulletin of Symbolic Logic 2 (2):199-213.
    We announce and explain recent results on the computably enumerable (c.e.) sets, especially their definability properties (as sets in the spirit of Cantor), their automorphisms (in the spirit of Felix Klein's Erlanger Programm), their dynamic properties, expressed in terms of how quickly elements enter them relative to elements entering other sets, and the Martin Invariance Conjecture on their Turing degrees, i.e., their information content with respect to relative computability (Turing reducibility).
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  10. S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare (1991). The D.R.E. Degrees Are Not Dense. Annals of Pure and Applied Logic 55 (2):125-151.
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  11. John T. Baldwin & Leo Harrington (1987). Trivial Pursuit: Remarks on the Main Gap. Annals of Pure and Applied Logic 34 (3):209-230.
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  12. Gregory Cherlin, Leo Harrington & Alistair H. Lachlan (1985). ℵ< Sub> 0-Categorical, ℵ< Sub> 0-Stable Structures. Annals of Pure and Applied Logic 28 (2):103-135.
     
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  13. Leo Harrington & Saharon Shelah (1985). Some Exact Equiconsistency Results in Set Theory. Notre Dame Journal of Formal Logic 26 (2):178-188.
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  14. Victor Harnik & Leo Harrington (1984). Fundamentals of Forking. Annals of Pure and Applied Logic 26 (3):245-286.
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  15. Leo A. Harrington & Alexander S. Kechris (1981). On the Determinacy of Games on Ordinals. Annals of Mathematical Logic 20 (2):109-154.
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  16. Fred G. Abramson & Leo A. Harrington (1978). Models Without Indiscernibles. Journal of Symbolic Logic 43 (3):572-600.
    For T any completion of Peano Arithmetic and for n any positive integer, there is a model of T of size $\beth_n$ with no (n + 1)-length sequence of indiscernibles. Hence the Hanf number for omitting types over T, H(T), is at least $\beth_\omega$ . (Now, using an upper bound previously obtained by Julia Knight H (true arithmetic) is exactly $\beth_\omega$ ). If T ≠ true arithmetic, then $H(T) = \beth_{\omega1}$ . If $\delta \not\rightarrow (\rho)^{ , then any completion of (...)
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  17. Leo Harrington (1978). Analytic Determinacy and 0#. [REVIEW] Journal of Symbolic Logic 43 (4):685 - 693.
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  18. Solomon Feferman, Jon Barwise & Leo Harrington (1977). Meeting of the Association for Symbolic Logic: Reno, 1976. Journal of Symbolic Logic 42 (1):156-160.
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  19. Leo Harrington (1977). Long Projective Wellorderings. Annals of Mathematical Logic 12 (1):1-24.
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  20. Jeff Paris & Leo Harrington (1977). A Mathematical Incompleteness in Peano Arithmetic. In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co.. 90--1133.
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  21. Leo Harrington & Thomas Jech (1976). On $Sigma_1$ Well-Orderings of the Universe. Journal of Symbolic Logic 41 (1):167-170.
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  22. Leo Harrington & Thomas Jech (1976). On Σ1 Well-Orderings of the Universe. Journal of Symbolic Logic 41 (1):167 - 170.
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  23. Leo A. Harrington & Alexander S. Kechris (1975). On Characterizing Spector Classes. Journal of Symbolic Logic 40 (1):19-24.
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  24. Leo Harrington (1974). Recursively Presentable Prime Models. Journal of Symbolic Logic 39 (2):305-309.
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